
Notice that in the above that non-zero correction terms suffice only for the second order moments (with indices 3, 4 and 5), which are related to the viscous stress tensor. In Eq. (REF ) and (REF ), the components of the raw moment equilibria for the square lattice \(\mathbf {m}^{eq,r}\)  follow via the binomial transformation of the corresponding central moment equilibria obtained via matching the respective continuous central moments of the Maxwell distribution function, which read as [1]}
\(m^{eq,r}_0&=& \eta ^{eq,r}_0= \rho ,\nonumber \\m^{eq,r}_1&=& \eta ^{eq,r}_x= \rho u_x,\nonumber \\m^{eq,r}_2&=&\eta ^{eq,r}_y= \rho u_y,\nonumber \\m^{eq,r}_3&=&\eta ^{eq,r}_{xx+yy}= 2 \rho c_s^2+ \rho (u_x^2+ u_y^2 ),\nonumber \\m^{eq,r}_4&=&\eta ^{eq,r}_{xx-yy}= \rho (u_x^2- u_y^2 ),\nonumber \\m^{eq,r}_5&=&\eta ^{eq,r}_{xy}= \rho u_x u_y,\nonumber \\m^{eq,r}_6&=&\eta ^{eq,r}_{xxy}= c_s^2 \rho u_y+ \rho u_x^2 u_y,\nonumber \\m^{eq,r}_7&=&\eta ^{eq,r}_{xyy}= c_s^2 \rho u_x+ \rho u_x u_y^2,\nonumber \\m^{eq,r}_8&=&\eta ^{eq,r}_{xxyy}= \rho c_s^4 + 3 \rho c_s^2 (u_x^2+ u_y^2 )+ \rho u_x^2 u_y^2,\) 
